Alex Jones

Fix shallow water equation

1

Instability found in following solution, what could be causing this? ```julia using ModelingToolkit, MethodOfLines, DomainSets, OrdinaryDiffEq using Plots using IfElse # Define the system of equations @parameters t x @variables...

These are currently unsupported, see #80 for example code

Implement recognition of `du0` for second order in time PDEs

We probably want sumnation by parts: See [DEO #506](https://github.com/SciML/DiffEqOperators.jl/issues/506) This could be implemented relatively quickly by leveraging this [package](https://github.com/ranocha/SummationByPartsOperators.jl)

Cannot find parent of var - 2nd order system problem - sol[u]

3

Solution retrieval fails with second order system: ```julia # Packages and inclusions using ModelingToolkit using OrdinaryDiffEq using ModelingToolkit: Differential # Parameters, variables, and derivatives @parameters t @variables (u(..))[1:6] D =...

Higher order nonuniform interpolation

6

Hi, I'm using Interpolations.jl over in [MethodOfLines.jl](https://github.com/SciML/MethodOfLines.jl), and am finding it very convenient for providing an interpolating interface to the solutions of PDES there. The solutions that it produces are...

System Transformation - Automatically make PDESystems compatible

2

Allows - Mixed derivatives - Composite derivative arguments - Time agnostic BC/IC parsing - More free choice of ic equation structure - Arbitrary order time derivatives - Expandable derivative terms...

At the moment WENO completely replaces upwind, but only first order is implemented. WENO should fall back on upwind for unimplemented orders.

Add ArrayDifferentialOperators for Vector calculus

7

Adds Vector calculus operators which are composable by the dot and cross product. A request for comment on a good design so that equations with these display intelligibly